Training neural networks is a complex task of great importance in problems of supervised learning. The Particle Swarm Optimization (PSO) consists of a stochastic global search originated from the attempt to graphically simulate the social behavior of a flock of birds looking for resources. In this work we analyze the use of the PSO algorithm and two variants with a local search operator for neural network training and investigate the influence of the GL_5 stop criteria in generalization control for swarm optimizers. For evaluating these algorithms we apply them to benchmark classification problems of the medical field. The results showed that the hybrid PSO with local search operator had the best results among the particle swarm optimizers and that the GL_5 stop criteria almost always degraded the performance of population based optimizers.